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Question
A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of 500 ms–1 in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground ______.
Options
remains the same because 500 ms−1 is very much smaller than vrms of the gas.
remains the same because motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls.
will increase by a factor equal to `(v_(rms)^2 + (500)^2)/v_(rms)^2` where vrms was the original mean square velocity of the gas.
will be different on the top wall and bottom wall of the vessel.
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Solution
A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of 500 ms–1 in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground remains the same because motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls.
Explanation:
According to the ideal gas law,
P = nRT/V, here temperature of the vessel remains unchanged hence, the pressure remains the same from that point of view.
Now, let us discuss the phenomenon inside the vessel. The gas molecules keep on colliding among themselves as well as with the walls of containing vessel. These collisions are perfectly elastic.
The number of collisions per unit volume in a gas remains constant. So, the pressure of the gas inside the vessel remains the same because the motion of the vessel as a whole does not affect the relative motion of the gas molecules with respect to the walls.
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